# The average of n numbers x1 x2 xn is overline x…

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### The average of n numbers x1, x2…..xn is $$\overline x$$ .Then the value of $$\sum\limits_{i\, = \,1}^n {} \left( {{x_i} – \overline x } \right)$$   is equal to –

1. A. n
2. B. 0
3. C. n$${\overline x }$$
4. D. $${\overline x }$$

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### Solution(By ExamCraze Team)

According to the question,
Average of 'n' number's x1, x2.....xn is $$overline x$$
Sum of n numbers = n$${overline x }$$
∴ $$sumlimits_{i, = ,1}^n {} left( {{x_1} - overline x } right)$$
Put i = 1, 2, 3.....n then
{x1 + x2 + x3 + .....(xn - n$${overline x }$$)}
As we know that
x1 + x2 + x3+.....+ xnx = n$${overline x }$$
= (n$${overline x }$$ - n$${overline x }$$)
= 0